AMC 12 2025a Problem 22

Three real numbers are chosen independently and uniformly at random between $0$ and $1$. What is the probability that the greatest of these three numbers is greater than $2$ times each of the other two numbers? (In other words, if the chosen numbers are $a \geq b \geq c$, then $a > 2b$.)

\textbf{(A)}\frac{1}{12} \textbf{(B)}\frac19 \textbf{(C)}\frac18 \textbf{(D)}\frac16 \textbf{(E)}~\frac14